Automatic image rejection calibration for radar systems using quadrature transceivers

ABSTRACT

A method of automatic image rejection and monitoring of a frequency modulated continuous-wave (FMCW) radar system, includes generating a quadrature FMCW signal comprising an in-phase signal and a quadrature signal by a dual output FMCW signal generator. The in-phase signal and the quadrature signal are transmitted. A radar signal comprising a response in-phase and a quadrature signal is received in response to the transmitted in-phase signal and the quadrature signal. The response in-phase signal and quadrature signals are provided to an analog to digital converter (ADC). An in-phase beat signal (Beat-I) and a quadrature beat signal (Beat-Q) are extracted from the ADC, based on a received windowing signal. A relative phase and/or amplitude adjustment is generated by providing a phase calibration variable (θ t ) and/or an amplitude calibration variable (A t ) as input to the dual output FMCW signal generator, based on a correlation between the Beat-I and the Beat-Q.

BACKGROUND Technical Field

The present disclosure generally relates to radar systems, and moreparticularly, to systems and methods of calibrating quadratureimbalances in Frequency-Modulated Continuous Wave radar systems.

Description of the Related Art

Frequency-Modulated Continuous Wave (FMCW) radar relates to radarsystems that radiate continuous transmission power and can change itsoperating frequency during a measurement by modulating its transmissionsignal in frequency and/or in phase. Typical FMCW radar systems are notused for wireless communications. In contrast, FMCW radar systems thatuse a quadrature transmitter TX and/or transceiver TRX can be configuredto be used for wireless communication. Such systems often transmit datausing a baseband interface with two ports: an in-phase (I) andquadrature (Q), these two signals are being mixed using an up-conversionmixer using with a high frequency signal and its quadrature,accordingly, to transform the base frequency signal to a much higherfrequency. The combined output is then transmitted by an antenna. Anopposite process is performed in the receive side, where adown-conversion mixer provides generates an I and Q outputs. An IQquadrature transceiver includes, for each transmitter (TX) or receiver(RX) separate paths for the I-channel and the Q-channel.

In order to use an IQ transceiver for FMCW radar, the baseband IQsignals are phased-shifted relative to each other by 90 degrees,sometimes referred to as a quadrature relationship. This has two mainbenefits: (i) cutting the bandwidth needed by half, and (ii) avoidingsignal modulation due to a rotation of IQ on a receive side.

SUMMARY

According to one embodiment, a frequency modulated continuous-wave(FMCW) radar system includes a quadrature transceiver comprising atransmitter having an in-phase input and a quadrature input and areceiver having an in-phase output and a quadrature output. A dualchannel FMCW signal generator includes a first output coupled to thein-phase input of the transmitter, and a second output coupled to thequadrature input of the transmitter. A first splitter is coupled betweenthe first output of the dual channel FMCW signal generator and thein-phase input of the transmitter. A second splitter is coupled betweenthe second output of the dual channel FMCW signal generator and thequadrature input of the transmitter. A first mixer includes a firstinput coupled to a second output of the first splitter; a second inputcoupled to the in-phase output of the receiver; and an output. A secondmixer includes a first input coupled to a second output of the secondsplitter; a second input coupled to the quadrature output of thereceiver; and an output. A dual channel analog to digital converter(ADC) includes a first input coupled to the output of the first mixer,and a second input coupled to the output of the second mixer. Acontroller is coupled between the programmable dual channel FMCW signalgenerator and the dual channel ADC.

In one embodiment, the dual channel FMCW signal generator isprogrammable.

In one embodiment, the dual channel FMCW is configured to provide awindowing signal that indicates a start and an end of each frequencyramp cycle.

In one embodiment, the first and second power splitters are two-waypower splitters.

In one embodiment, the controller includes a quadrature calibrationblock that is configured to receive an in-phase beat signal from a firstoutput of the dual channel ADC and a quadrature beat signal from asecond output of the dual channel ADC.

In one embodiment, there is a low pass filter at each input channel ofthe dual channel ADC.

In one embodiment, the controller further comprises a Fast FourierTransform (FFT) block configured to receive the in-phase beat signal andthe quadrature beat signal from the second output of the dual channelADC and to provide a radar output. In one embodiment, pre or post FFTaveraging of the Beat-I and Beat-Q signals can be used to improve thesignal to noise ratio (SNR). In this way, the signal to noise ratio ofthe radar output is improved.

In one embodiment, the quadrature calibration block is configured toprovide at least one of a phase calibration variable (θt) or anamplitude calibration variable (A_(t)) as input to the dual output FMCWsignal generator.

In one embodiment, the dual channel FMCW signal generator is a digitalcircuit block.

In one embodiment, the controller is configured to select initialquadrature calibration variables (θ_(t), A_(t)). The initial quadraturecalibration variables (θ_(t), A_(t)) are applied as input to the dualoutput FMCW signal generator. An in-phase beat signal from a firstoutput of the dual channel ADC and a quadrature beat signal from asecond output of the dual channel ADC are received, based on the appliedinitial quadrature calibration variables (θ_(t), A_(t)). The in-phasebeat signal is correlated with the quadrature beat signal. Upondetermining that the correlation is below a predetermined threshold, newquadrature calibration variables (θ_(t), A_(t)) are selected.

According to one embodiment, a method of automatic image rejection of afrequency modulated continuous-wave (FMCW) radar system includesgenerating a quadrature FMCW signal comprising an in-phase signal and aquadrature signal by a dual output FMCW signal generator. The in-phasesignal and the quadrature signal are transmitted by way of a transmitterof a transceiver. A radar signal comprising a response in-phase signaland a response quadrature signal are received in response to thetransmitted in-phase signal and the quadrature signal of thetransceiver. The response in-phase signal and the response quadraturesignal are provided to a dual channel analog to digital converter (ADC).A controller receives a windowing signal that indicates a start and anend of a frequency ramp cycle of the generated quadrature FMCW signal.The controller extracts an in-phase beat signal (Beat-I) and aquadrature beat signal (Beat-Q) from the dual channel ADC, based on areceived windowing signal. The controller correlates between the Beat-Iand the Beat-Q. The controller generates a relative phase and/oramplitude adjustment by providing a phase calibration variable (θ_(t))and/or an amplitude calibration variable (A_(t)) as input to the dualoutput FMCW signal generator, based on the correlation.

In one embodiment, upon determining that a threshold correlation is notachieved, the phase calibration variable (θ_(t)) and/or the amplitudecalibration variable (A_(t)) is iteratively adjusted and provided asinput to the dual output FMCW signal generator, until the thresholdcorrelation is achieved.

In one embodiment, low pass filtering is performed at each input channelof the dual channel ADC.

In one embodiment, the in-phase signal of the FMCW signal is split by afirst power splitter into a first in-phase signal of the FMCW signalthat is provided to the transmitter and a second in-phase signal of theFMCW signal as a first in-phase input to a first mixer. The quadraturesignal of the FMCW signal is split by a second power splitter into afirst quadrature signal of the FMCW signal that is provided to thetransmitter and a second quadrature signal of the FMCW signal as a firstquadrature input to a second mixer.

In one embodiment, the first mixer mixes the first in-phase input withan in-phase radar signal received by the receiver and provides a resultas a first input to a dual channel analog to digital converter (ADC).The second mixer mixes the first quadrature input with a quadratureradar signal received by the receiver and provides a result as a secondinput to the dual channel ADC.

In one embodiment, at least one of a direction of the transmitter or thereceiver is adjusted to increase a leakage current or amount of signalreflection to enhance a calibration capability of the FMCW radar system.

According to one embodiment, a method of calibrating a frequencymodulated continuous-wave (FMCW) radar system includes providing aquadrature transceiver comprising a transmitter having an in-phase inputand a quadrature input, and a receiver having an in-phase output and aquadrature output. A dual channel FMCW signal generator is providedcomprising a first output coupled to the in-phase input of thetransmitter, and a second output coupled to the quadrature input of thetransmitter. A first splitter is coupled between the first output of thedual channel FMCW signal generator and the in-phase input of thetransmitter. A second splitter is coupled between the second output ofthe dual channel FMCW signal generator and the quadrature input of thetransmitter. A first mixer provided comprising a first input coupled toa second output of the first splitter, a second input coupled to thein-phase output of the receiver, and an output. A second mixer isprovided comprising a first input coupled to a second output of thesecond splitter, a second input coupled to the quadrature output of thereceiver and an output. A dual channel analog to digital converter (ADC)is provided comprising a first input coupled to the output of the firstmixer, and a second input coupled to the output of the second mixer. Acontroller is coupled between the programmable dual channel FMCW signalgenerator and the dual channel ADC.

In one embodiment, the dual channel FMCW signal generator receives aphase calibration variable (θ_(t)) and/or an amplitude calibrationvariable (A_(t)). The dual channel FMCW signal generator is programmedbased on the received phase calibration variable (θ_(t)) and/or theamplitude calibration variable (A_(t)).

In one embodiment, a windowing signal is provided by the dual channelFMCW signal generator, which indicates a start and an end of eachfrequency ramp cycle of the dual channel FMCW signal generator.

In one embodiment, a quadrature calibration block of the controllerreceives an in-phase beat signal from a first output of the dual channelADC and a quadrature beat signal from a second output of the dualchannel ADC.

In one embodiment, each input channel of the dual channel ADC is lowpass filtered.

In one embodiment, a Fast Fourier Transform (FFT) block of thecontroller receives the quadrature beat signal from the second output ofthe dual channel ADC and provides a radar output based on the quadraturebeat signal.

In one embodiment, at least one of a phase calibration variable (θ_(t))or an amplitude calibration variable (A_(t)) is provided as input to thedual output FMCW signal generator, by the quadrature calibration blockof the controller.

In one embodiment, the FMCW signal generator is operated in a digitalrealm.

In one embodiment, the controller selects initial quadrature calibrationvariables (θ_(t), A_(t)). The controller applies the initial quadraturecalibration variables (θ_(t), A_(t)) as input to the dual output FMCWsignal generator. The controller receives an in-phase beat signal from afirst output of the dual channel ADC and a quadrature beat signal from asecond output of the dual channel ADC based on the applied initialquadrature calibration variables (θ_(t), A_(t)). The controllercorrelates the in-phase beat signal with the quadrature beat signal.Upon determining that the correlation is below a predeterminedthreshold, the controller selects new quadrature calibration variables(θt, At) to be applied to the dual output FMCW signal generator.

The techniques described herein may be implemented in a number of ways.Example implementations are provided below with reference to thefollowing figures.

BRIEF DESCRIPTION OF THE DRAWINGS

The drawings are of illustrative embodiments. They do not illustrate allembodiments. Other embodiments may be used in addition or instead.Details that may be apparent or unnecessary may be omitted to save spaceor for more effective illustration. Some embodiments may be practicedwith additional components or steps and/or without all of the componentsor steps that are illustrated. When the same numeral appears indifferent drawings, it refers to the same or like components or steps.

FIG. 1 is a block diagram of an architecture of a calibration of anin-phase and quadrature path imbalance for a frequency modulatedcontinuous-wave radar system using a quadrature transceiver, consistentwith an illustrative embodiment.

FIG. 2 is a conceptual block diagram of a calibration of an in-phase andquadrature imbalance for an FMCW radar system, consistent with anillustrative embodiment.

FIG. 3 provides an example table for a path to be used for the phase andamplitude calibration variables θ_(t) and A_(t) pattern, consistent withan illustrative embodiment.

FIG. 4 provides a more detailed block diagram of an architecture of acalibration of an in-phase and quadrature path imbalance for a frequencymodulated continuous-wave radar system using a quadrature transceiver,consistent with an illustrative embodiment.

FIG. 5A illustrates an example spectrum response of the output of aquadrature transmitter TX before calibration.

FIG. 5B illustrates an example spectrum response of the output of aquadrature transmitter TX after calibration.

FIG. 6 presents an example processes, consistent with an illustrativeembodiment.

FIG. 7 provides a functional block diagram illustration of a computerhardware platform that can be used to implement a particularlyconfigured computing device.

DETAILED DESCRIPTION Overview

In the following detailed description, numerous specific details are setforth by way of examples in order to provide a thorough understanding ofthe relevant teachings. However, it should be apparent that the presentteachings may be practiced without such details. In other instances,well-known methods, procedures, components, and/or circuitry have beendescribed at a relatively high-level, without detail, in order to avoidunnecessarily obscuring aspects of the present teachings.

The present disclosure generally relates to radar systems, and moreparticularly, to systems and methods of calibrating quadratureimbalances in Frequency-Modulated Continuous Wave radar systems.

Quadrature imbalance in the transmitter or receiver can weaken theability to successfully transmit and/or receive high speed data carriedby the wireless signal. For example, quadrature imbalance may occur whenthe phase relationship between the I and Q channels is not exactly 90degrees and/or the amplitude of the I channel is different from that ofthe Q channel. Accordingly, quadrature imbalance can be caused by gainand/or phase mismatches of the high frequency components in the I and Qchannels of an FMCW radar system. For example, the receiver componentsin the I channel can have slightly different phase and/or amplitude thanthe receiver components in the Q channel, thereby introducing imbalanceor mismatch errors in the I and Q baseband signals. Although thedifferences are usually small, these gain and phase imbalances reducethe quality of the FMCW radar system, double the bandwidth, and canincrease the number of bit errors for a given data rate.

Known FMCW radar systems that use a quadrature architecture typicallyinvolve a generation of a frequency ramp in quadrature using a dualchannel Direct Digital Synthesizer (DDS) with up to 500M samples persecond, allowing a narrower 200 MHz bandwidth. Further, knownarchitectures typically involve a large bandwidth and are costly toimplement, often involving a field programmable gate array (FPGA) thatfeeds a dual channel Digital to Analog Converter (ADC), or applicationspecific integrated circuit (ASIC) to feed two streams of data, andresult in high power consumption. However, such systems typically onlyfocus on providing a good dual channel FMCW in quadrature, but do notprovide automatic image rejection calibration and monitoring. Poor imagerejection results in transmission of signal at image frequencies, whichultimately result in radar response modulation.

The teachings herein are able to accommodate quadrature imbalance in thereceiver and/or transmitter, which can facilitate transmission andreceipt of high-speed data carried by the wireless radar signal. Gainand/or undesired phase mismatches between the in-phase and quadraturepaths are systematically removed by way of an image rejectioncalibration. A quadrature FMCW signal is generated. Two radar readingsare received from a dual channel analog to digital converter (ADC). Awindowing signal is used to extract an in-phase beat signal and aquadrature beat signal, sometimes referred to herein as Beat-I andBeat-Q. A correlation between the two channels is performed anditeratively repeated until the correlation between the Beat-I and Beat-Qsignals is within a predetermined threshold or a maximum correlation isachieved. By virtue of concepts discussed herein continuous validationand tracking on the image rejection performance is provided. A wiredloop between the transmitter and the receiver, or external measurementequipment is not required. The features of the present application willbe better understood in view of FIGS. 1 to 4 , which are discussed indetail below.

Example Architecture

FIG. 1 is a block diagram of an architecture 100 of a calibration of anin-phase and quadrature path imbalance for a frequency modulatedcontinuous-wave (FMCW) radar system using a quadrature transceiver,consistent with an illustrative embodiment. Architecture 100 includes atransceiver 108 having an in-phase input “I” and a quadrature input “Q,”which are provided to a transmitter (TX) 110 of the quadraturetransceiver 108. The quadrature transceiver 108 has a receiver (RX) 112having an in-phase output “I” and a quadrature output “Q.” In variousembodiments, the transceiver can support various communication protocolsthat use OFDM signals, including, without limitation, 802.11a/g/n(WiFi), 802.16d/e/m (WiMAX), and 3GPP Rel. 8/9 (LTE).

There is a dual channel FMCW signal generator 102 having a first outputcoupled to the in-phase input I of the transmitter 110 and a secondoutput coupled to the quadrature input Q of the transmitter 110. Thedual channel FMCW signal generator 102 is programmable in phase andamplitude based on input calibration signals of phase and amplitude(θ_(t), A_(t)) received from the controller 140, discussed in moredetail later. The dual channel FMCW signal generator 102 is configuredto provide a windowing signal that indicates a start and an end of eachfrequency ramp cycle 138 to the controller 140. For simplicity and toavoid clutter, various elements of the transmitter have been omitted,such as, multiplexers, power sources, local oscillators, digital signalprocessing (DSP) elements, etc.

By virtue of being generated in the digital realm, the frequency ramp138 generated by the dual output FMCW signal generator 102 is digitallytimed and synchronized using a common clock running at 3.5 GHz and anyrelative shift between them, due to line delay and internal buffer, isfixed and therefore consistent and accurate. For such ramp generation isnot subject to process variations, temperature of operation, etc.,typically experienced by analog circuit blocks.

The output of the dual output FMCW signal generator is an in-phasesignal and a quadrature signal (TX IQ FMCW), represented by equations 1and 2 below:

$\begin{matrix}{{{In}{Phase}}\rightarrow{\cos\left( {2{\pi\left( {f_{0} + {\frac{bw}{T}t}} \right)}t} \right)}} & \left( {{Eq}.1} \right)\end{matrix}$ $\begin{matrix}{{Quadrature}\rightarrow{\sin\left( {2{\pi\left( {f_{0} + {\frac{bw}{T}t}} \right)}t} \right)}} & \left( {{Eq}.2} \right)\end{matrix}$

Where

-   -   f₀ is the start frequency;    -   T is the period;    -   bw is the bandwidth; and    -   t is the time from when ramp starts, values between 0 to T . . .

As mentioned previously, the dual output FMCW signal generator 102 isprogrammable, which allows the in-phase and/or quadrature path to beadjusted. For example, equation 3 below provides a quadrature path thatcan be adjusted based on calibration variables (θ_(t), A_(t)).

$\begin{matrix}{{Quadrature}\rightarrow{A_{t}{\sin\left( {{2{\pi\left( {f_{0} + {\frac{bw}{T}t}} \right)}t} + \theta_{t}} \right)}}} & \left( {{Eq}.3} \right)\end{matrix}$

As illustrated in equation 3 above, the quadrature path has a phasecalibration variable θ_(t) and an amplitude calibration variable A_(t),which allow adjustment of the quadrature (and/or in-phase) signal thatis provided to the transmitter 110 of the transceiver 108. As usedherein, for simplicity, the parameter A_(t) represents a relativeamplitude with respect to the quadrature path and the in-phase path.These calibration variables are provided by the controller 140 ascalibration signals, as will be discussed in more detail below.

There is a first power splitter 104 coupled between the first output ofthe dual channel FMCW signal generator 102 and the in-phase input I ofthe transmitter 110. There is a second power splitter 106 coupledbetween the second output of the dual channel FMCW signal generator 102and the quadrature Q input of the transmitter 110. The first and secondpower splitters 104 and 106 are two-way power splitters in that theyeach split the signal received from an output of the dual channel FMCWsignal generator 102 and divide it between the transmitter and acorresponding mixer 120 or 122, respectively, in the receiver RX 112feedback path, discussed in more detail below.

For example, the first splitter 104 is configured to receive thein-phase signal from the dual output FMCW signal generator 102 and splitit into two separate paths, one leading to an in-phase input I of thetransmitter 110 of the quadrature transceiver 108, and the second to thefirst mixer 120. The output of the receiver 112 (i.e., RX IQ FMCW) whenthe image rejection is near perfect for the in-phase output and thequadrature output of the receiver 112 is provided by equations 4 and 5,respectively:

$\begin{matrix}{{{In}{Phase}}\rightarrow{\cos\left( {2\pi\left( {f_{0} + {\frac{bw}{T}\left( {t - \tau} \right)}} \right)\left( {t - \tau} \right)} \right)}} & \left( {{Eq}.4} \right)\end{matrix}$ $\begin{matrix}{{Quadrature}\rightarrow{\sin\left( {2{\pi\left( {f_{0} + {\frac{bw}{T}\left( {t - \tau} \right)}} \right)}\left( {t - \tau} \right)} \right)}} & \left( {{Eq}.5} \right)\end{matrix}$

Equations 4 and 5 above represent the RX IQ FMCW when image rejection isnear perfect. By way of example only and not by way of limitation, a 1.4GHz bandwidth using a 3.5GSPS Direct Digital Synthesizer (DDS) can beused as part of the dual output FMCW signal generator 102. In oneembodiment, two DDS are used for the dual output FMCW signal generator102.

The first mixer 120 has a first input coupled to a second output of thefirst two-way splitter 104. There is a second input coupled to thein-phase output I of the receiver 112. Similarly, the second mixer 122includes a first input coupled to a second output of the second two-waysplitter 106 and a second input coupled to the quadrature output Q ofthe receiver 112. Each of the first and second mixers 120 and 122provide an output that is provided to a dual channel analog to digitalconverter 130.

The first mixer 120 mixes the split in-phase signal received from thefirst splitter 104 with the in-phase output I of the receiver 112.Similarly, the second mixer 122 mixes the split quadrature signal fromthe second splitter 106 with the quadrature output Q of the receiver112. The output of both mixers 120 and 122 is provided to a dual channelanalog to digital converter 130 that is configured to provide anin-phase beat signal (sometimes referred to herein as Beat-I) and aquadrature signal (sometimes referred to herein as Beat-Q). The dualchannel analog to digital converter 130 includes a first input coupledto the output of the first mixer 120 and a second input coupled to theoutput of the second mixer 122. The Dual channel ADC receives thesignals from the mixers 120 and 122 and provides a correspondingin-phase and quadrature output signals, sometimes referred to herein asBeat-I and Beat-Q. It should be noted that, in one embodiment, a samerelatively slow ADC (e.g., 10KSPS-10MSPS) that is used for a typicalradar pipeline, is supported by the teachings herein, thereby reducingdesign complexity and cost. In some embodiments, there is a low passfilter (not shown) at each input of the dual channel ADC 130. Equations6 and 7 provide the Beat IQ FMCW signals, respectively, withoutfiltration.cos α*cos β=1/2(cos(α−β)+cos (α+β))   (Eq. 6)sin α*sin β=1/2(cos(α−β)+cos (α+β))   (Eq. 7)

When applying low pass filtration (LPF) at the output of the dualchannel ADC 130, the following expressions are obtained:cos α*cos β=1/2(cos(α−β))   (Eq. 8)sin α*sin β=1/2(cos(α−β))   (Eq. 9)

In one example, the bandwidth that is provided at the output of the dualchannel ADC 130 is 100 KHz to 2 MHz. By virtue of having such arelatively low frequency, a less complex and lower cost ADC 130 can beused.

The architecture includes a controller 140 coupled between the dualchannel FMCW signal generator 102 and the dual channel ADC 130. In oneembodiment, the controller 140 includes a quadrature calibration block142 that is configured to receive the in-phase beat signal (Beat-I) froma first output of the dual channel ADC and a quadrature beat signal(Beat-Q) from a second output of the dual channel ADC 130. Thecontroller 140 further includes a Fast Fourier Transform (FFT) block 144configured to receive the quadrature beat signal from the second outputof the dual channel ADC and to provide a radar output. The FFT block 144is a practical use of FMCW processing pipeline, which allows the systemto detect reflection from various distances. Each single tone representsa response from a corresponding distance. Every bin step is equivalentto the range resolution, which is dictated by the bandwidth. Thequadrature calibration block 142 provides calibration signals of phaseand amplitude (θ_(t), A_(t)) as an input to the dual channel FMCW signalgenerator 102.

Example Quadrature Calibration

Reference now is made to FIG. 2 , which provides a conceptual blockdiagram 200 of a calibration of an in-phase and quadrature imbalance foran FMCW radar system, consistent with an illustrative embodiment. Manyof the blocks are repeated here from FIG. 1 for perspective andtherefore not repeated here for brevity. Additional detail is providedin reference to the quadrature calibration block 142 of the controller140 that was mentioned previously in the context of the discussion ofFIG. 1 .

At block 240 of the quadrature calibration block 142, a table having apredetermined path for calibration of the phase and calibrationvariables θ_(t) and A_(t), is provided. In various embodiments,different techniques can be used to provide the calibration values forθ_(t) and A_(t). By way of non-limiting example, a brute force approachmay be used by filling a table and choosing the option with the highestcorrelation value; a coarse to fine approach may be used by startingwith a coarse estimate (e.g., bigger steps) and zooming in to regionswith higher potential; a memory could be used to store previous valuesand refine around them to support PVT variation, etc.

Reference is made to FIG. 3 , which provides an example table 300 for apath to be used for the calibration values θ_(t) and A_(t), sometimesreferred to herein as a virtual loop or a snake pattern, consistent withan illustrative embodiment. It will be understood that table 300 isprovided herein by way of example only, and not by way of limitation, asother ways of generating the calibration variables θ_(t) and A_(t) aresupported by the teachings herein as well.

Different values of θ_(t) and A_(t) can be iteratively applied from thetable 300 until a threshold calibration is achieved. The horizontal axis302 represents an increment/decrement in phase value θ_(t), whereas thevertical axis 304 represents an increment/decrement of amplitude valueA_(t). For example, the initial calibration variables may be based on(θ_(t) and A_(t))=(0, 1) represented by Corr1. In the next iteration,variables (∂θ_(t), 1) are applied, represented by Corr2, and so on,until a desired threshold correlation or maximum correlation is achievedbetween the in-phase path and the quadrature path, as indicated by theBeat-I and Beat-Q signals, explained in more detail below. While a snakemethod is provided, it will be understood that the present teachings arenot limited thereto. Other techniques can be used as well.

Referring back to FIG. 2 , at block 242, the initial quadraturecalibration variables (θ_(t), A_(t)) of the table 300 are used toinitiate calibration. As explained above, the initial correlationvariables may be set to, for example, (0, 1). These variables 252 areapplied to the dual output FMCW signal generator 102 to receive feedbackfrom the feedback loop of the system of FIG. 2 .

At block 244, the Beat-I and Beat-Q output received from the dualchannel ADC 130 is used to perform a correlation of these two outputs(i.e., correlation between the two beating signals Beat-I and Beat-Q).Expression 10 below provides an example correlation:M(θ_(t) ,A _(t))=MAC(Beat-I, Beat-Q)/L   (Eq. 10)

Where L is the length of the common correlation vector of Beat-I andBeat-Q

One correlation is performed for each frequency ramp used to frequencymodulate (FM) the FMCW radar system. In one example, a DDS function of aDigital Ramp generator (DRG) is used. The ramp generation parametersallow the user to control both the rising and falling slopes of theramp. The upper and lower boundaries of the ramp, the step size and steprate of the rising portion of the ramp, and the step size and step rateof the falling portion of the ramp, can be all programmable. Calibrationis based on the similarity between Beat-I and Beat-Q signals from thedual channel DAC 130, identified by the multiply and accumulateoperation (MAC) between the “beat signals” Beat-I and Beat-Q, performedby the quadrature calibration module 142.

At block 246, a comparison is performed and a determination is madewhether the correlation is within a predetermined threshold. Equations11 and 12 below provide example expressions:If M(θ_(max), A_(max))<M(θ_(t),A_(t))   (Eq. 11)θ_(max),A_(max)=θ_(t),A_(t)   (Eq. 12)

For example, the above operations are used to align and verify that theimage rejection is optimal or within a predetermined threshold. To thatend, the received radar responses in I & Q paths, represented by theBeat-I and Beat-Q signals provided by the dual channel ADC 130 arecompared. For example, if the goal is to maximize the similarity betweenthese to beat signals, the correlation between the Beat-I and Beat-Qsignals is measured. A linear swift of the relative phase between thetransmitted signals may be provided, starting with a classical 90degrees.

If a threshold correlation is not achieved (i.e., “No” at decision blockdecision block 248, the process returns to block 242 and a next phaseand amplitude calibration variable pair is used (e.g., from thereference table 300 of FIG. 3 ) and the iterative process continues. Forexample, an additional iteration is performed with introduction ofamplitude variation and/or phase variation between the signals.

However, if the correlation is within the predetermined threshold (whichcould be maximum), then the appropriate quadrature calibration variable(θ_(t), A_(t)) pair is adopted as the appropriate (e.g., maximum)variables to be applied 250 as the selected variables 252. In variousembodiments, this quadrature calibration can be applied to the in-phasepath or the quadrature path. Accordingly, the dual channel programmablesignal generator 102 is used to generate two signals in quadrature,where one path is adjusted with the respect to the other. Calibration isbased on the similarity between Beat-I and Beat-Q. In this way, a moreaccurate correlation between these two paths is provided.

It should be noted that, for calibration purposes, the naturallyoccurring leakage 210 between the TX 110 and the RX 112 can be enhancedby way of beam steering in scenarios where the environment is notconducive to measure reflections. In case that the radar response isweak, (e.g., radar is facing the sky), the phases in RX 112 and TX 110can be set to increase cross-talk, by creating an antenna-based loopthat would produce strong radar response. For example, in oneembodiment, the beam direction of the TX 110 and/or RX 112 can beadjusted (e.g., TX to transmit down (i.e., towards the direction of theRX) and/or the receiver RX is adjusted to sense up (e.g., in thedirection of the TX)) to expound the leakage current in order to be ableto evaluate the calibration capability of the system 200.

Reference now is made to FIG. 4 , which provides a more detailed blockdiagram 400 of an architecture of a calibration of an in-phase andquadrature path imbalance for a frequency modulated continuous-waveradar system using a quadrature transceiver, consistent with anillustrative embodiment. Many of the components in FIG. 4 are similar tothose of FIG. 1 and therefore not repeated for brevity. In theembodiment of FIG. 4 , the architecture indicates how the use of twosingle-output DDSs can be accommodated.

In the initialization, both direct digital synthesizers (DDSs) are beingprogrammed with identical ramp parameters, such as ramp rate, step size,and bandwidth. The salient parameter that is different from theembodiment of FIG. 1 is that the one connected to in-phase is generatinga cosine and the one connected to quadrature is generating a sine.

As illustrated in FIG. 4 , a Clock Distribution integrated circuit (IC)402 provides a reference clock to both DDSs 404 and 406, avoiding theuse of internal phased locked loop (PLL). Two separate DDS (i.e., 404and 406) are used in the architecture of FIG. 4 . In the embodiment ofFIG. 4 , a divided clock of the DDS system clock is to generate asynchronized control of the digital ramp for both DDSs 404 and 406.

The DDS is providing an output signal of when the ramp starts and ends(DROVR) at 410 and 412, respectively. In case that the received signalis not strong enough, the controller steers the TX 110 and RX 112towards each other.

The ADC 130 receives the output of the mixers 120, 122, and has adigital input for the ramp indicator signal that is synchronized withthe two analog inputs. The controller 140 uses the ramp indicator signalto crop both analog inputs for further calculation of correlationvalues.

By virtue of the teachings herein, better image rejection is achievedbetween the TX 110 and the RX 112. In one aspect, verification of actualimage rejection on low frequency signals is already available in thebeating signals Beat-I and Beat-Q, without the need to use a manualspectrum analyzer or a dedicated circuit at high frequency. In oneembodiment, the system of FIG. 2 provides continuous tracking of thequality of received signals by way of the feedback provided by theBeat-I and Beat-Q signals that are evaluated by the quadraturecalibration block 142.

Example Results

Reference now is made to FIGS. 5A and 5B, which illustrate the spectrumresponse of the output of a quadrature receiver RX before and aftercalibration, respectively. As illustrated in FIG. 5A, the initial I andQ are set to cosine and sine accordingly before system calibration andthe TX image therefor is not suppressed. By way of contrast, FIG. 5Billustrates a system level calibrated with right amplitude and phasecompensation for I and Q outputs being the same based on the teachingsherein, thereby resulting in an approximate 25 dB TX image suppression.

Example Process

With the foregoing overview of the example architectures 100, 200, and400, it may be helpful now to consider a high-level discussion of anexample process. To that end, FIG. 6 presents a process 600 of a methodof automatic image rejection of a frequency modulated continuous-waveradar system, consistent with an illustrative embodiment. Process 600 isillustrated as a collection of blocks in a logical flowchart, whichrepresents sequence of operations that can be implemented in hardware,software, or a combination thereof. In the context of software, theblocks represent computer-executable instructions that, when executed byone or more processors of a controller, perform the recited operations.Generally, computer-executable instructions may include routines,programs, objects, components, data structures, and the like thatperform functions or implement abstract data types. In each process, theorder in which the operations are described is not intended to beconstrued as a limitation, and any number of the described blocks can becombined in any order and/or performed in parallel to implement theprocess. For discussion purposes, the process 600 is described withreference to the architecture 100 of FIG. 1 .

At block 602, a quadrature FMCW signal comprising an in-phase signal anda quadrature signal is generated by a dual output FMCW signal generator102.

At block 604, the in-phase signal and the quadrature signal aretransmitted by way of a transmitter TX 110 of a transceiver 108.

At block 606, a radar reading comprising a response in-phase signal anda response quadrature signal is received in response to the transmittedin-phase signal and the quadrature signal of the transceiver 108.

At block 608, the response in-phase signal and the response quadraturesignal are provided to a dual channel analog to digital converter (ADC)130.

At block 610, the controller 140 receives a windowing signal thatindicates a start and an end of a frequency ramp cycle of the generatedquadrature FMCW signal.

At block 612, the controller 140 extracts an in-phase beat signal(Beat-I) and a quadrature beat signal (Beat-Q) from the dual channel ADC130, based on a received windowing signal 140.

At block 614, the controller 140 correlates between the Beat-I and theBeat-Q.

At block 616, a determination is made whether the correlation is above apredetermined threshold. If so (i.e., “YES” at determination block 616),the controller continues with block 618 where the controller sets arelative phase and/or amplitude adjustment by providing a phasecalibration variable (θ_(t)) and/or an amplitude calibration variable(A_(t)) as input to the dual output FMCW signal generator, based on thecorrelation.

If not, (i.e., “NO” at determination block 616), the process continueswith block 620, where the controller determines a new relative phaseand/or amplitude adjustment by providing a new phase calibrationvariable (θ_(t)) and/or a new amplitude calibration variable (A_(t)) asinput to the dual output FMCW signal generator. The iterative processthen returns to block 602 and continues until the correlation is above apredetermined threshold.

Example Computer Platform

As discussed above, functions relating to automatic image rejection of afrequency modulated continuous-wave radar system, as shown in FIGS. 1,2, and 4 , and in accordance with process 600 FIG. 6 , may involve acontroller or processor. In this regard, FIG. 7 provides a functionalblock diagram illustration of a computer hardware platform 700 that canbe used to implement a particularly configured computing device thatcould implement the controller of FIG. 1 .

The computer platform 700 may include a central processing unit (CPU)704, a hard disk drive (HDD) 706, random access memory (RAM) and/or readonly memory (ROM) 708, a keyboard 710, a mouse 712, a display 714, and acommunication interface 716, which are connected to a system bus 702.

In one embodiment, the HDD 706, has capabilities that include storing aprogram that can execute various processes, such as the quadraturecalibration engine 740, in a manner described herein. The quadraturecalibration engine 740 may have various modules configured to performdifferent functions, such those discussed in the context of FIG. 1 andothers. For example, there may be an interaction module 742 operative tointeract with a dual channel ADC to extract an in-phase and/orquadrature beat therefrom. There may be a calibration variablegeneration module 744 configured to generate an appropriate quadraturecalibration variable θ_(t) and/or A_(t) to be used as an input to a dualoutput FMCW signal generator. In various embodiments, the quadraturecalibration variables θ_(t) and/or A_(t) can be calculated and/orretrieved from a reference table by way of following a snake pattern, asdescribed herein.

In one embodiment, there is a digital filtration module operative to lowpass filter out the signals received from the dual channel ADC. Theremay be an FFT module 748 operative to provide a radar output based on areceived quadrature beat signal from the dual channel ADC.

While modules 742 to 748 are illustrated in FIG. 7 to be part of the HDD706, in some embodiments, one or more of these modules may beimplemented in the hardware of the computing device 700. For example,the modules discussed herein may be implemented in the form of partialhardware and partial software. That is, one or more of the components ofthe Quadrature calibration engine 740 shown in FIG. 7 may be implementedin the form of electronic circuits with transistor(s), diode(s),capacitor(s), resistor(s), inductor(s), varactor(s) and/or memristor(s).In other words, Quadrature calibration engine 740 may be implementedwith one or more specially-designed electronic circuits performingspecific tasks and functions described herein.

Conclusion

The descriptions of the various embodiments of the present teachingshave been presented for purposes of illustration, but are not intendedto be exhaustive or limited to the embodiments disclosed. Manymodifications and variations will be apparent to those of ordinary skillin the art without departing from the scope and spirit of the describedembodiments. The terminology used herein was chosen to best explain theprinciples of the embodiments, the practical application or technicalimprovement over technologies found in the marketplace, or to enableothers of ordinary skill in the art to understand the embodimentsdisclosed herein.

While the foregoing has described what are considered to be the beststate and/or other examples, it is understood that various modificationsmay be made therein and that the subject matter disclosed herein may beimplemented in various forms and examples, and that the teachings may beapplied in numerous applications, only some of which have been describedherein. It is intended by the following claims to claim any and allapplications, modifications and variations that fall within the truescope of the present teachings.

The components, steps, features, objects, benefits and advantages thathave been discussed herein are merely illustrative. None of them, northe discussions relating to them, are intended to limit the scope ofprotection. While various advantages have been discussed herein, it willbe understood that not all embodiments necessarily include alladvantages. Unless otherwise stated, all measurements, values, ratings,positions, magnitudes, sizes, and other specifications that are setforth in this specification, including in the claims that follow, areapproximate, not exact. They are intended to have a reasonable rangethat is consistent with the functions to which they relate and with whatis customary in the art to which they pertain.

Numerous other embodiments are also contemplated. These includeembodiments that have fewer, additional, and/or different components,steps, features, objects, benefits and advantages. These also includeembodiments in which the components and/or steps are arranged and/orordered differently. For example, any signal discussed herein may bescaled, buffered, scaled and buffered, converted to another state (e.g.,voltage, current, charge, time, etc.,), or converted to another state(e.g., from HIGH to LOW and LOW to HIGH) without materially changing theunderlying control method.

Aspects of the present disclosure are described herein with reference toflowchart illustrations and/or block diagrams of methods, apparatus(systems), and computer program products according to embodiments of theapplication. It will be understood that each block of the flowchartillustrations and/or block diagrams, and combinations of blocks in theflowchart illustrations and/or block diagrams, can be implemented bycomputer readable program instructions.

These computer readable program instructions may be provided to aprocessor of a general-purpose computer, special purpose computer, orother programmable data processing apparatus to produce a machine, suchthat the instructions, which execute via the processor of the computeror other programmable data processing apparatus, create means forimplementing the functions/acts specified in the flowchart and/or blockdiagram block or blocks. These computer readable program instructionsmay also be stored in a computer readable storage medium that can directa computer, a programmable data processing apparatus, and/or otherdevices to function in a particular manner, such that the computerreadable storage medium having instructions stored therein comprises anarticle of manufacture including instructions which implement aspects ofthe function/act specified in the flowchart and/or block diagram blockor blocks.

The computer readable program instructions may also be loaded onto acomputer, other programmable data processing apparatus, or other deviceto cause a series of operational steps to be performed on the computer,other programmable apparatus or other device to produce a computerimplemented process, such that the instructions which execute on thecomputer, other programmable apparatus, or other device implement thefunctions/acts specified in the flowchart and/or block diagram block orblocks.

The flowchart and block diagrams in the Figures illustrate thearchitecture, functionality, and operation of possible implementationsof systems, methods, and computer program products according to variousembodiments of the present invention. In this regard, each block in theflowchart or block diagrams may represent a module, segment, or portionof instructions, which comprises one or more executable instructions forimplementing the specified logical function(s). In some alternativeimplementations, the functions noted in the blocks may occur out of theorder noted in the Figures. For example, two blocks shown in successionmay, in fact, be executed substantially concurrently, or the blocks maysometimes be executed in the reverse order, depending upon thefunctionality involved. It will also be noted that each block of theblock diagrams and/or flowchart illustration, and combinations of blocksin the block diagrams and/or flowchart illustration, can be implementedby special purpose hardware-based systems that perform the specifiedfunctions or acts or carry out combinations of special purpose hardwareand computer instructions.

While the foregoing has been described in conjunction with exemplaryembodiments, it is understood that the term “exemplary” is merely meantas an example, rather than the best or optimal. Except as statedimmediately above, nothing that has been stated or illustrated isintended or should be interpreted to cause a dedication of anycomponent, step, feature, object, benefit, advantage, or equivalent tothe public, regardless of whether it is or is not recited in the claims.

It will be understood that the terms and expressions used herein havethe ordinary meaning as is accorded to such terms and expressions withrespect to their corresponding respective areas of inquiry and studyexcept where specific meanings have otherwise been set forth herein.Relational terms such as first and second and the like may be usedsolely to distinguish one entity or action from another withoutnecessarily requiring or implying any actual such relationship or orderbetween such entities or actions. The terms “comprises,” “comprising,”or any other variation thereof, are intended to cover a non-exclusiveinclusion, such that a process, method, article, or apparatus thatcomprises a list of elements does not include only those elements butmay include other elements not expressly listed or inherent to suchprocess, method, article, or apparatus. An element proceeded by “a” or“an” does not, without further constraints, preclude the existence ofadditional identical elements in the process, method, article, orapparatus that comprises the element.

The Abstract of the Disclosure is provided to allow the reader toquickly ascertain the nature of the technical disclosure. It issubmitted with the understanding that it will not be used to interpretor limit the scope or meaning of the claims. In addition, in theforegoing Detailed Description, it can be seen that various features aregrouped together in various embodiments for the purpose of streamliningthe disclosure. This method of disclosure is not to be interpreted asreflecting an intention that the claimed embodiments require morefeatures than are expressly recited in each claim. Rather, as thefollowing claims reflect, inventive subject matter lies in less than allfeatures of a single disclosed embodiment. Thus, the following claimsare hereby incorporated into the Detailed Description, with each claimstanding on its own as a separately claimed subject matter.

What is claimed is:
 1. A frequency modulated continuous-wave (FMCW)radar system comprising: a quadrature transceiver comprising: atransmitter having an in-phase input and a quadrature input; and areceiver having an in-phase output and a quadrature output; a dualchannel FMCW signal generator having two direct digital synthesizers(DDSs), comprising: a first output coupled to the in-phase input of thetransmitter; and a second output coupled to the quadrature input of thetransmitter; a first splitter coupled between the first output of thedual channel FMCW signal generator and the in-phase input of thetransmitter; a second splitter coupled between the second output of thedual channel FMCW signal generator and the quadrature input of thetransmitter; a first mixer comprising: a first input coupled to a secondoutput of the first splitter; a second input coupled to the in-phaseoutput of the receiver; and an output of the first mixer; a second mixercomprising: a first input coupled to a second output of the secondsplitter; a second input coupled to the quadrature output of thereceiver; and an output of the second mixer; a dual channel analog todigital converter (ADC) comprising: a first input coupled to the outputof the first mixer; and a second input coupled to the output of thesecond mixer; and a controller coupled between the dual channel FMCWsignal generator and the dual channel ADC.
 2. The FMCW radar system ofclaim 1, wherein the dual channel FMCW signal generator is programmable.3. The FMCW radar system of claim 1, wherein the dual channel FMCW isconfigured to provide a windowing signal that indicates a start and anend of each frequency ramp cycle.
 4. The FMCW radar system of claim 1,wherein the controller comprises a quadrature calibration block that isconfigured to receive an in-phase beat signal from a first output of thedual channel ADC and a quadrature beat signal from a second output ofthe dual channel ADC.
 5. The FMCW radar system of claim 4, furthercomprising a low pass filter at each input channel of the dual channelADC.
 6. The FMCW radar system of claim 4, wherein the controller furthercomprises a Fast Fourier Transform (FFT) block configured to receive thein-phase beat signal and the quadrature beat signal from the secondoutput of the dual channel ADC and to provide a radar output having animproved signal to noise ratio (SNR).
 7. The FMCW radar system of claim4, wherein the quadrature calibration block is configured to provide atleast one of a phase calibration variable (θ_(t)) or an amplitudecalibration variable (A_(t)) as input to the dual output FMCW signalgenerator.
 8. The FMCW radar system of claim 1, wherein the dual channelFMCW signal generator is a digital circuit block.
 9. The FMCW radarsystem of claim 1, wherein the controller is configured to: selectinitial quadrature calibration variables (θ_(t), A_(t)); apply theinitial quadrature calibration variables (θ_(t), A_(t)) as input to thedual output FMCW signal generator; receive an in-phase beat signal froma first output of the dual channel ADC and a quadrature beat signal froma second output of the dual channel ADC based on the applied initialquadrature calibration variables (θ_(t), A_(t)); correlate the in-phasebeat signal with the quadrature beat signal; and upon determining thatthe correlation is below a predetermined threshold, select newquadrature calibration variables (θ_(t), A_(t)).
 10. A method ofautomatic image rejection of a frequency modulated continuous-wave(FMCW) radar system, comprising: generating a quadrature FMCW signalcomprising an in-phase signal and a quadrature signal by a dual outputFMCW signal generator; transmitting the in-phase signal and thequadrature signal by way of a transmitter of a transceiver; receiving aradar signal comprising a response in-phase signal and a responsequadrature signal in response to the transmitted in-phase signal and thequadrature signal of the transceiver; providing the response in-phasesignal and the response quadrature signal to a dual channel analog todigital converter (ADC); receiving, by a controller, a windowing signalthat indicates a start and an end of a frequency ramp cycle of thegenerated quadrature FMCW signal; extracting, by the controller, anin-phase beat signal (Beat-I) and a quadrature beat signal (Beat-Q) fromthe dual channel ADC, based on the received windowing signal;correlating, by the controller, between the Beat-I and the Beat-Q; andgenerating, by the controller, a relative phase and/or amplitudeadjustment by providing a phase calibration variable (θ_(t)) and/or anamplitude calibration variable (A_(t)) as input to the dual output FMCWsignal generator, based on the correlation.
 11. The method of claim 10,further comprising upon determining that a threshold correlation is notachieved, iteratively adjusting the phase calibration variable (θ_(t))and/or the amplitude calibration variable (A_(t)) as input to the dualoutput FMCW signal generator, until the threshold correlation isachieved.
 12. The method of claim 10, further comprising: splitting thein-phase signal of the FMCW signal by a first power splitter into afirst in-phase signal of the FMCW signal that is provided to thetransmitter and a second in-phase signal of the FMCW signal as a firstin-phase input to a first mixer; and splitting the quadrature signal ofthe FMCW signal by a second power splitter into a first quadraturesignal of the FMCW signal that is provided to the transmitter and asecond quadrature signal of the FMCW signal as a first quadrature inputto a second mixer.
 13. The method of claim 12, further comprising:mixing, by the first mixer, the first in-phase input with an in-phaseradar signal received by the receiver and providing a result as a firstinput to the dual channel analog to digital converter (ADC); and mixing,by the second mixer, the first quadrature input with a quadrature radarsignal received by the receiver and providing a result as a second inputto the dual channel ADC.
 14. The method of claim 10, further comprisingadjusting at least one of a direction of the transmitter or the receiverto increase a signal reflection to enhance a calibration capability ofthe FMCW radar system.
 15. A method of calibrating a frequency modulatedcontinuous-wave (FMCW) radar system comprising: providing a quadraturetransceiver comprising a transmitter having an in-phase input and aquadrature input, and a receiver having an in-phase output and aquadrature output; providing a dual channel FMCW signal generator havingtwo direct digital synthesizers (DDSs) and comprising a first outputcoupled to the in-phase input of the transmitter, and a second outputcoupled to the quadrature input of the transmitter; coupling a firstsplitter between the first output of the dual channel FMCW signalgenerator and the in-phase input of the transmitter; coupling a secondsplitter between the second output of the dual channel FMCW signalgenerator and the quadrature input of the transmitter; providing a firstmixer comprising a first input coupled to a second output of the firstsplitter, a second input coupled to the in-phase output of the receiver,and an output of the first mixer; providing a second mixer comprising afirst input coupled to a second output of the second splitter, a secondinput coupled to the quadrature output of the receiver and an output ofthe second mixer; providing a dual channel analog to digital converter(ADC) comprising a first input coupled to the output of the first mixer,and a second input coupled to the output of the second mixer; andcoupling a controller between the dual channel FMCW signal generator andthe dual channel ADC.
 16. The method of claim 15, further comprising:receiving, by the dual channel FMCW signal generator, a phasecalibration variable (θ_(t)) and/or an amplitude calibration variable(A_(t)); and programming the dual channel FMCW signal generator based onthe received phase calibration variable (θ_(t)) and/or the amplitudecalibration variable (A_(t)).
 17. The method of claim 15, furthercomprising providing a windowing signal, by the dual channel FMCW signalgenerator, which indicates a start and an end of each frequency rampcycle of the dual channel FMCW signal generator.
 18. The method of claim15, further comprising receiving, by a quadrature calibration block ofthe controller, an in-phase beat signal from a first output of the dualchannel ADC and a quadrature beat signal from a second output of thedual channel ADC.
 19. The method of claim 18, further comprisingproviding at least one of a phase calibration variable (θ_(t)) or anamplitude calibration variable (A_(t)) as input to the dual output FMCWsignal generator, by the quadrature calibration block of the controller.20. The method of claim 15, further comprising: selecting, by thecontroller, initial quadrature calibration variables (θ_(t), A_(t));applying, by the controller, the initial quadrature calibrationvariables (θ_(t), A_(t)) as input to the dual output FMCW signalgenerator; receiving, by the controller, an in-phase beat signal from afirst output of the dual channel ADC and a quadrature beat signal from asecond output of the dual channel ADC based on the applied initialquadrature calibration variables (θ_(t), A_(t)); correlating, by thecontroller, the in-phase beat signal with the quadrature beat signal;and upon determining that the correlation is below a predeterminedthreshold, selecting, by the controller, new quadrature calibrationvariables (θ_(t), A_(t)) to be applied to the dual output FMCW signalgenerator.